[PPT] - Outline Formal Modeling of Flexible Processes in Mobile Ad-hoc PowerPoint Presentation

SLIDE 1

Formal Modeling of Flexible Processes in Mobile Ad-hoc Networks with Algebraic Higher-Order Nets

Institut f¨ ur Softwaretechnik und theoretische Informatik Technische Universit¨ at Berlin

May 2007

Outline

◮ motivation and basic ideas ◮ example: emergency scenario ◮ nets and rules as token ◮ algebraic higher-order nets ◮ modeling workflows in MANETs ◮ conclusion

Modeling Workflows in Mobile Ad-hoc Networks

◮ network of mobile devices ◮ team members communicate with one another via wireless links

without relying on an underlying infrastructure

◮ team members execute sets of activities modeled as workflows ◮ MANETs topology both influences and is influenced by the

workflow

◮ modeling workflow modifications as required by topology

transformations

requirements for the modeling technique

Emergency Scenario: Archaeological Site after an Earthquake

Museum Precarious Bell-Tower Building Church

Hit Area

Picture Store Operator Bridge Team Leader Camera

Movement needed to accomplish the task Movement needed to maintain the network connectivity; should be adaptively driven by the cooperative application

Cooperation with MOBIDIS – Universit´ a di Roma ”La Sapienza” WORKPAD – EU-project (8 sites)

SLIDE 2

System Architecture

Mobile Device j

Service 3 Service 4 Network Service Interface Wireless Stack (802.11x, Bluetooth)

Mobile Device i

Service 1 Service 2 Network Service Interface Wireless Stack (802.11x, Bluetooth)

Mobile Device Coordinator

Wireless Stack (802.11x, Bluetooth) Network Service Interface Coordination Layer Predictive Layer Workflow Adapter Workflow Execution Engine Rewriting Rules Workflow Schema

Mobile Device j

Service 3 Service 4 Network Service Interface Wireless Stack (802.11x, Bluetooth)

Mobile Device i

Service 1 Service 2 Network Service Interface Wireless Stack (802.11x, Bluetooth)

Mobile Device Coordinator

Wireless Stack (802.11x, Bluetooth) Network Service Interface Coordination Layer Predictive Layer Workflow Adapter Workflow Execution Engine Rewriting Rules Workflow Schema

Mobile Device j

Service 3 Service 4 Network Service Interface Wireless Stack (802.11x, Bluetooth)

Mobile Device j

Service 3 Service 4 Network Service Interface Wireless Stack (802.11x, Bluetooth)

Mobile Device i

Service 1 Service 2 Network Service Interface Wireless Stack (802.11x, Bluetooth)

Mobile Device i

Service 1 Service 2 Network Service Interface Wireless Stack (802.11x, Bluetooth)

Mobile Device Coordinator

Wireless Stack (802.11x, Bluetooth) Network Service Interface Coordination Layer Predictive Layer Workflow Adapter Workflow Execution Engine Rewriting Rules Workflow Schema

Mobile Device Coordinator

Wireless Stack (802.11x, Bluetooth) Network Service Interface Coordination Layer Predictive Layer Workflow Adapter Workflow Execution Engine Rewriting Rules Workflow Schema

◮ modeling at the coordination layer ◮ modeling of the distributed workflows ◮ abstraction from the technical infrastructure

Cooperation with MOBIDIS – Universit´ a di Roma ”La Sapienza” WORKPAD – EU-project (8 sites)

Modeling Workflows and Transformations in MANETs

◮ applying algebraic approaches based on

algebraic higher-order nets with Petri nets, graphs and rules as tokens

◮ algebraic higher-order net coordinates

workflow execution and rule application

◮ a team consists of a workflow and its topology graph ◮ rules are tuples of net and graph rules

Execution Workflow Workflow Teams Rules Adaption

Workflow Execution

PN1

Team

Start Compile Questionnaire Go to Destination Select Building

Execution Workflow

enabled(s, t) = true s fire(s, t)

signature and algebra for

◮ Reconfigurable Petri

systems, i.e. P/T-nets with markings

◮ firing behavior ◮ and net transformations

Workflow Execution

Start Compile Questionnaire Go to Destination Select Building

PN1’

Team

fire(s, t)

Execution Workflow

enabled(s, t) = true s

signature and algebra for

◮ Reconfigurable Petri

systems, i.e. P/T-nets with markings

◮ firing behavior ◮ and net transformation

SLIDE 3

Workflow Adaption

I1

Go to Destination Follow Team Member 3 Send Photos

R1

Send Photos

Rule Team

Go to Destination

L1 SystemRules ∧(transform.(r1, m1)) = s′ (cod.(m1)) = s Workflow Adaption r1 ∧(dom.(c′)) = (trans.(s′)) s′ s Teams

Workflow Adaption

I1 Zoom on damaged part Capture Scene Go to Destination Send Photos Zoom on damaged part Capture Scene Go to Destination Send Photos Follow Team Member 3 Go to Destination Follow Team Member 3 Send Photos Go to Destination Send Photos PN2 K1 PN1 Select Building Matching Zoom on damaged part Capture Scene Select Building Matching Select Building Matching R1 L1

signature and algebra for

◮ Petri system rules ◮ transformation of systems

Formale Modellierung und Analyse flexibler Processe in mobilen ad-hoc Netzwerken

2006 – 2008 funded by the

http://tfs.cs.tu-berlin.de/formalnet/

◮ MANETs:

research focus mainly on technical infrastructure in this project: modeling of workflows in the MANETs

◮ process modeling:

various approaches, e.g. process algebras, activity-, flow-, or state-charts, Petri nets, adaptive workflows, ... in this project: algebraic higher-order nets

◮ formal modeling and adaption of workflows in MANETs:

in this project: reconfigurable Petri nets; Project Leaders: H. Ehrig, J. Padberg, K. Hoffmann

Main tasks of

◮ characterization of main properties ◮ suitable restriction of AHO nets ◮ structuring and transformation in AHO nets ◮ process modeling and analysis in AHO nets ◮ methodology and (prototypes of) tool support

GOAL:

adequate specification technique for multi-level modeling of workflows in MANETs

SLIDE 4

Reconfigurable P/T-systems

◮ algebraic approach to

Petri (net) systems

◮ algebraic approach to

net transformations

◮ based on

weak adhesive HLR systems

P/T-systems

Definition (P/T-systems PS = (N, M0) )

◮ a net N = (P, T, pre, post) with

◮ a set of places P ◮ a set of transistions T ◮ weighted arcs pre, post : T → P⊕

◮ the initial marking M0 ∈ P⊕ ◮ P/T-morphism f = (fP, fT) : PS1 → PS2

with fP : P1 → P2 and fT : T1 → T2 s.t.

◮ f ⊕

P ◦ pre1 = pre2 ◦ fT and f ⊕ P ◦ post1 = post2 ◦ fT

◮ f ⊕

P (M0 1|p) ≤ M0 2|fP(p) for p ∈ P1

◮ firing PS = (N, M) t

− → (N, M′) = PS′ where M[t > M′ in net N

Rule application

Definition (Net transformation)

A rule rule = (L

l

← − K

r

− → R) with P/T-systems L, K, and R, and two strict injections K

l

− → L and K

r

− → R is applicable at match L

m

− → PS1 if the gluing condition holds leading to a direct transformation PS1

rule

= ⇒ PS2 consisting of the pushouts (1) and (2): L

m

(1)

K

l

r
(2)

R

PS1

PS′

1

PS2

Concurrent situation

firing steps

Select Building Matching

(N0,M0)

Go to Destination Send Photos Make Photo

− →

Select Building Matching Go to Destination Send Photos Make Photo

(N0,M0’)

− →

Select Building Matching Go to Destination Send Photos Make Photo

(N0,M0’)

SLIDE 5

Concurrent situation

transformation steps

Select Building Matching

(N0,M0)

Go to Destination Send Photos Make Photo

= ⇒

Send Photos Make Photo Select Building Matching (N1,M1) Follow Camera Device Go to Destination

= ⇒

Select Building Matching Zoom on damaged part Capture Scene Go to Destination Send Photos Device Follow Camera (N2,M2)

Independence and conflict

(N0, M′′′

0 )

(N0, M′

0) t2

rule1,m′

1)

(N1, M′

1)

(N0, M′′

0 ) t1

(rule2,m′

2)

(N0, M0)

t2

(rule1,m1)
t1
(rule2,m2)
(1)

(2) (3) (4)

(N1, M1)

t1

(rule2,m′′

2 )

(N2, M′

2)

(N2, M2)

t2

(rule1,m′′

1 )

(N3, M3) square (1) classical Petri net notion: conflict/conflict free square (4) classical graph transformation notion: parallel independence square (2) square (3) new situation: parallel independence

f transformation and firing step

Main results for square (2) and (3)

Definition (Parallel Independence)

A transformation and a firing step are parallel independent if (1) the transition is not deleted by the transformation step and (2) enough tokens are left by the firing step.

Theorem

Given parallel independent steps (PN0, M0) = ⇒ (PN1, M1) and (PN0, M0) − → (PN0, M′

0)

then the square is commuting (PN0, M0)

(PN0, M′

0)

(PN1, M1)
(PN1, M′

1)

Main result in Petri Nets’07 paper

Main Results for square (4)

Theorem

The category (PTSys, Mstrict) is a weak adhesive HLR category. Main results for weak adhesive HLR categories:

1. Local Church-Rosser Theorem,
2. Parallelism Theorem,
3. Concurrency Theorem.

Main result in Petri Nets’07 paper

SLIDE 6

P/T-Systems and Rules as Tokens

P/T-System sys Token Game rule Transformation L I R Rule

◮ new paradigm ”nets and rules as tokens”

as reconfigurable nets

◮ integration of token game and rule-based

transformation of P/T-systems into AHO-Nets

◮ stepwise development of P/T-systems

based on the double-pushout approach

Signature and Algebra for Reconfiburable P/T-Systems

◮ vocabularies T0 for transitions and P0 for places ◮ set ASystem: all P/T-systems over T0 and P0 ◮ set AMor: all P/T-system morphisms

◮ mappings of places resp. transitions ◮ compatible with environment ◮ preservation of marking

◮ set ARules: all rules of P/T-systems with strict injections ◮ (fire.(PN, t))A computes the follower marking ◮ (transform.(r, m))A computes direct transformation

Definition ( AHON-SIG Signature)

Given vocabularies T0 and P0, the signature HLNR-SYSTEM-SIG is given by HLNR-SYSTEM-SIG = sorts: Transitions, Places, Bool, System, Mor, Rules

pns:

tt, ff :→ Bool enabled : System × Transitions → Bool fire : System × Transitions → System applicable : Rules × Mor → Bool transform : Rules × Mor → System coproduct : System × System → System isomorphic : System × System → Bool cod : Mor → System

Definition ( AHON-SIG Algebra (Carrier sets))

The AHON-SIG-algebra A for reconfigurable P/T-systems is given by

◮ ATransitions = T0, APlaces = P0, ABool = {true, false}, ◮ ASystem the set of all P/T-systems over T0 and P0, i.e.

ASystem = {PN = (P, T, pre, post, M)} ∪ {undef} P/T-systems with P ⊆ P0, T ⊆ T0

◮ AMor the set of all P/T-morphisms for ASystem, i.e.

AMor = {f : PN → PN′},

◮ ARules the set of all rules of P/T-systems, i.e.

ARules = {r = (L

i1

← − I

i2

− → R)} with strict inclusions i1, i2

SLIDE 7

Definition ( AHON-SIG Algebra (Functions))

The AHON-SIG-algebra A for reconfigurable P/T-systems is given by

◮ ttA = true, ffA = false ◮ enabledA(PN, t) =

true

if t ∈ T, pre(t) ≤ M false else

◮ fireA(PN, t) =

⎧ ⎪ ⎨ ⎪ ⎩ (P, T, pre, post, M ⊖ pre(t) ⊕ post(t)) if enabledA(PN, t) = true undef else

Definition ( AHON-SIG Algebra (Functions ff))

The AHON-SIG-algebra A for reconfigurable P/T-systems is given by

◮ applicableA(r, m) =

true

if r is applicable at match m false else

◮ transformA(r, m) =

H

if applicableA(r, m) undef else where for L

m

− → G and applicableA(r, m) = true we have a direct transformation G

r

= ⇒ H,

Definition ( AHON-SIG Algebra (Functions ff))

The AHON-SIG-algebra A for reconfigurable P/T-systems is given by

◮ coproductA(PN1, PN2) =

if (PN1 = undef ∨ PN2 = undef) then undef else ((P1 ⊎ P2), (T1 ⊎ T2), pre3, post3, M1 ⊕ M2)

◮ isomorphicA(PN1, PN2) =

true

if PN1 ∼ = PN2 false else

◮ codA : AMor → ASystem with codA (f : PN1 → PN2) = PN2.

Main Results - Algebraic Higher-Order Nets

◮ clear and mathematically well-founded formalism of Algebraic

Higher-Order Nets

◮ net category with specification fixed morphisms ◮ suitable semantics given by firing step semantics and

higher-order processes

◮ preservation of the firing behavior by morphisms ◮ structuring techniques union and fusion, supporting composition

and identification of subnets

SLIDE 8

Modeling workflows in MANETs

◮ separating different views with different granularity ◮ layered architecture for modeling workflows in MANETs ◮ distribution of workflows

leads to

◮ questions of consistency and maintaining consistency ◮ notion of consistent layer environment ◮ construction of new consistent layer environment after rule

applications

◮ restoring consistency

Layered Architecture

◮ workflow in MANETs consists of

three different aspects

◮ general activities concerning the workflow

⇒ workflow layer

◮ local view of team members

⇒ team layer

◮ movement activities

⇒ mobility layer

◮ predictive layer signals probable disconnections

Layered architecture

Workflow Workflow Adaption Workflow Adaption Workflow Adaption

Team Layer

Workflow Execution Rules P/T−net Workflow Execution Rules P/T−net

Workflow Layer Mobility Layer

Workflow Execution Rules P/T−net Nets Mobility Net Team Member

◮ formalized by a layered

AHO net

◮ P/T-nets describe those activities

being relevant in a certain layer

◮ rules in a certain layer are

provided for transformation ⇒ question of consistency

Example: Layers

Select Building Make Photo Compile Questionnaire Matching Team Leader (picture store decive) Team Member 1 (camera device) Team Member 2 (bridge device)

= ⇒

Select Building Zoom on Capture Scene Send Photos damaged part Compile Questionnaire Matching Team Leader (picture store decive) Team Member 1 (camera device) Team Member 2 (bridge device)

Changes in the workflow layer

SLIDE 9

Example: Layers

(picture store device) Matching Select Building Team Leader Start Go to Destination Go to Destination Stop Zoom on Capture Scene Send Photos damaged part Team Member 1 (camera device) Go to Destination

Questionnaire (bridge device) Compile Team Member 2

= ⇒

Follow Member 3 Member 3 Follow Team Follow Member 3 Stop Compile Questionnaire Team Member 2 (bridge device) Start

Changes in the team layer

Example: Layers

Go to Destination Start Go to Destination Go to Destination Stop Team Leader (picture store decive) Team Member 1 (camera device) Team Member 2 (bridge device)

= ⇒

Start Go to Destination Member 3 Follow Team Follow Member 3 Stop Go to Destination Stop Team Leader (picture store decive) Team Member 1 (camera device) Team Member 2 (bridge device) Start Follow Member 3 Go to Destination

Changes in the mobility layer

Consistent Layer Environment

I

M
(PO)

W

T

tm1

αm1

tm2

αm2

◮ workflow W, mobility net M,

team members’ nets tmi

◮ (fixed) interface I, so that

teamwork net T = M +I W

◮ activity arrows tmi αmi

− → T

◮ refinement of places in W with subnets

f M

Independent transformation of each net!

Consistent Layer Environment and Tranformations

I

M0
r M
(PO)

W0

r W

T0

t1

α1

r1
t2

α2

r2
t3

α3

r3
M1

t1

1

t2

1

t3

1

W1

◮ checking consistency

in all states consistency can be checked

◮ guaranteed consistency

all states are a consistent one

◮ backtracking consistency

possibility of inconsistent states, but backtrack transformations

◮ restoring consistency

possibility of inconsistent states, but conditions for next transformations

SLIDE 10

New Consistent Layer Environment

I

M0
r M
W0
r W
M1
T0

r

W1
tm

αm

rm
tm

1 αm

1

T1

◮ consistent layer environment T0 = M0 +I W0 ◮ the transformations W0 r W

= ⇒ W1, M0

r M

= ⇒ M1 and the transformations tm

rm

= ⇒ tm

1 ◮ so that the layer consistency conditions hold

then new consistent layer environment T1 = M1 +I W1 Main result in FASE07-paper

Summary

◮ first ideas of AHO nets ◮ nets and rules as tokens ◮ modeling technique for flexible workflows in MANETs ◮ layered architecture for the AHO net model

Selected Publications

◮ H. Ehrig, K. Hoffmann, J. Padberg, et al. Independence of Net

Transformations and Token Firing in Reconfigurable Place/Transition Systems. Proc. of the Int. Conference on Application and Theory of Petri Nets and Other Models of Concurrency (Petri Nets’07), accepted.

◮ J. Padberg, K. Hoffmann, H. Ehrig et al. Maintaining Consistency in

Layered Architectures of Mobile Ad-hoc Networks Proc. of the Int. Conference on Fundamental Approaches to Software Engineering (FASE’07). Lecture Notes in Computer Science 4422, pp. 383-397, Springer, 2007.

◮ P

. Bottoni, F . De Rosa, K. Hoffmann, M. Mecella. Applying Algebraic Approaches for Modeling Workflows and their Transformations in Mobile Networks. Mobile Information Systems, 2006.

◮ K. Hoffmann, H. Ehrig, T. Mossakowski. High-Level Nets with Nets